Mathematics High School

## Answers

**Answer 1**

The **area **of this **parallelogram** is equal to 150 cm².

How to calculate the area of this parallelogram?

In Mathematics and Geometry, the area of a **parallelogram** can be calculated by using this formula:

Area of a parallelogram = b × h

Where:

b represent the base area of a **parallelogram**.h represent the** height** of a parallelogram.

By substituting the given parameters into the formula for the** area** of a **parallelogram**, we have the following;

Area of a parallelogram = 10 × 15

**Area** of a **parallelogram** = 150 cm².

In this context, we can logically deduce that the **area** of a parallelogram whose base area is 10 cm and **height** is 15 cm would be equal to 150 square centimeters.

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Complete Question:

Calculate the area of the parallelogram whose base is 10 cm and height is 15 cm.

## Related Questions

if the entire windows area is 1520.54 what is its radius

### Answers

For finding the** radius **we have to calculate by using the following formulae **A=πr²**. This will find the radius.

**What is radius?**

the separation between a circle's** centre **and circumference. Its **diameter **is **halves** that of the circle.

Now according to the question,

entire windows area is 1520.54

** ** A=πr²

1520.54 =(22/7)×r²

r = sqrt((1520.54×7)/22)

r=21.99

The** question **is:

If the entire area of the windows is 1520.54. What will be the radius of it?

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In a class of 40 students, 19 like singing, 17 like dancing and 13 like both singing and dancing.

Draw a Venn diagram to illustrate the information above

### Answers

I hope you like it. This is it

According to the Fundamental Theorem of Algebra, how many zeros does the function f(x) = 5x6+2x3−4x + 1 ?

### Answers

By the *Fundamental Theorem of Algebra,* the **function**, f(x) = 5x⁶ + 2x³ −4x + 1, has exactly 6 complex **zeros **(counting multiplicities)

Determining how many zeros has a function

From the question, we are to determine the **number of zeros the **given function has

From the given information,

The given function is

f(x) = 5x⁶ + 2x³ −4x + 1

From the* Fundamental Theorem of Algebra *which states that any polynomial function of degree n has exactly n complex zeros (counting multiplicities).

In this case, the degree of the polynomial function f(x) = 5x⁶ + 2x³ - 4x + 1 is 6.

Hence, the **function** has exactly 6 complex **zeros **(counting multiplicities).

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Determine the field property or axiom of equality used to justify each step. You may choose from the properties listed in the 2-column table.

### Answers

Below are the field properties or **axioms** of equality used to justify each step.

**What is an axiom answer?**

An **axiom** is a rule or statement that is generally accepted to be true without **proof**. An axiom is also called a **postulate**.

7(x + 3) = 4 + 3x

7x + 21 = 4 + 3x --- Distributive Property of Multiplication over Addition

7x + 21 = 3x + 4 --- Subtraction Property of Equality

4x + 21 = 4 ---- Commutative Property of Addition

4x = - 17 -------- Subtraction Property of Equality

1/4 * (4 * 1) = 1/4 * (- 17) ----- Multiplication Property of Equality

x = 1/4 * (- 17) ----- Multiplicative Identity Property

x =-17/4 ----- Multiplicative Inverse Property

Hence, Above are the field properties or **axioms** of equality used to justify each step.

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The purchase price of a new car bought by Kay Terchek is $30,875. The

car's MSRP was $32,560. Her other costs were sales tax at 7%, non-taxable

extended warranty at $390, registration fees at $128. Kay got a $250 rebate and

made a $4,300 down payment. What was the delivered price of the car and the

amount due?

### Answers

**Answer: The delivered price of the car was $30,943.85, and the amount due was $26,643.85.**

**Step-by-step explanation:**

To calculate the delivered price of the car, we need to add up all the costs associated with the purchase:

Purchase price = $30,875

Sales tax at 7% = 0.07 x ($30,875 - $250) = $2,080.25

Extended warranty = $390

Registration fees = $128

Total cost = $30,875 + $2,080.25 + $390 + $128 = $33,473.25

To calculate the amount due, we need to subtract the rebate and the down payment from the delivered price:

Delivered price = $33,473.25

Rebate = $250

Down payment = $4,300

Amount due = $33,473.25 - $250 - $4,300 = $29,923.25

However, the above calculation assumes that the sales tax is calculated based on the MSRP of the car. If the sales tax is instead calculated based on the purchase price, the delivered price and amount due will be slightly different. Here are the revised calculations:

Purchase price = $30,875

Sales tax at 7% = 0.07 x $30,875 = $2,161.25

Extended warranty = $390

Registration fees = $128

Total cost = $30,875 + $2,161.25 + $390 + $128 = $33,554.25

Delivered price = $33,554.25

Rebate = $250

Down payment = $4,300

Amount due = $33,554.25 - $250 - $4,300 = $29,004.25

So, depending on how the sales tax is calculated, the delivered price and amount due may vary slightly.

What would be the correct answer to this problem?

### Answers

**Step-by-step explanation:**

To find the total cost, we need to multiply the weight of each type of soup by its respective price per kilogram and then add up the costs.

The cost of 5 kg of chicken chili is:

5 kg * $0.83/kg = $4.15

The cost of 5 kg of tortilla soup is:

5 kg * $0.51/kg = $2.55

The cost of 3 kg of lobster bisque is:

3 kg * $2.02/kg = $6.06

The total cost of all three types of soup is:

$4.15 + $2.55 + $6.06 = $12.76

Therefore, the total cost of the soups is $12.76.

**Answer: **$12.76

**Step-by-step explanation:**

chicken chili = 0.83/kg

5kg x 0.83/kg = $4.15

tortilla soup = 0.51/kg

5kg x 0.51/kg = $2.55

lobster bisque =2.02/kg

3kg x 2.02/kg = $6.06

$4.15 + $2.55 + $6.06 = $12.76

The exact circumference of a circle is 18 π inches. What is the area of the circle? Express your answer in terms of π . __ in.2

### Answers

**Answer:**

25.7831

**Step-by-step explanation:**

A=πr2

C=2πr

Solving forA

A=C2

4π=182

4·π≈25.7831

Directions: Find the measure of the indicated angle to the nearest tenth of a degree.

X

39

10

### Answers

The **measure **of the** indicated angle**, given the right angled triangle and the dimensions, is 14.4 degrees .

How to find the measure of the angle ?

Given the position of the **angle **in this **right angled triangle**, we know that the dimensions available to us are the opposite and adjacent dimensions.

We can therefore use the **tangent rule **to solve for angle x such that the angle is:

Tan ( angle ) = Opposite / Adjacent

**Angle x** is therefore:

Tan (x ) = 10 / 39

x = Tan ⁻ ¹ ( 10 / 39 )

x = 14.4 degrees

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A student is graduating from college in 12 months but will need a loan in the amount of $11,985 for the last two semesters. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:

Unsubsidized Stafford Loan: annual interest rate of 3.85%, compounded monthly, and a grace period of six months from time of graduation

PLUS loan: annual interest rate of 4.15%, compounded monthly, with a balance of $12,491.95 at the time of repayment

Which loan will have a higher balance, and by how much at the time of repayment?

The PLUS loan will have a higher balance by $37.30 at the time of repayment.

The Stafford loan will have a higher balance by $37.30 at the time of repayment.

The PLUS loan will have a higher balance by $204.39 at the time of repayment.

The Stafford loan will have a higher balance by $204.39 at the time of repayment.

### Answers

The correct answer is: The **Stafford **loan will have a higher balance by **$835.39 **at the time of repayment.

**What is compound interest ?**

Compound interest is a type of interest that is calculated on the initial **principal **amount as well as the accumulated **interest **from previous **periods**. In other words, it is interest that is earned on both the principal amount and the interest already earned. The interest is added to the principal amount, and the new total amount then earns interest for the next period. This **cycle **continues until the end of the term or until the loan is paid off. The formula for compound interest takes into account the interest rate, the number of **compounding **periods per year, and the length of time the money is invested.

**According to the question:**To solve this problem, we need to calculate the balance of each loan at the time of repayment.

For the unsubsidized Stafford Loan, the total amount borrowed will be $11,985. Interest will be charged monthly at a rate of 3.85%/12 = 0.0032083. The loan will be repaid 6 months after graduation, so the number of monthly payments will be 6*12 = 72. Using the formula for the balance of a loan with monthly compounding, we get:

[tex]Balance = 11985*(1+0.0032083)^{72} = $13,190.34[/tex]

For the PLUS Loan, the total amount borrowed will be $12,491.95. Interest will be charged monthly at a rate of 4.15%/12 = 0.0034583. The loan will be repaid immediately after graduation, so the number of monthly payments will be 12. Using the formula for the balance of a loan with monthly compounding, we get:

[tex]Balance = 12491.95*(1+0.0034583)^{12} = $12,354.95[/tex]

Therefore, the PLUS loan will have a lower balance at the time of repayment, by $835.39.

The correct answer is: The Stafford loan will have a higher balance by $835.39 at the time of repayment.

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Find the area of the circle. Use 3.14 for π. Round your answer to the nearest hundredth.

A circle with radius 1.2 kilometers is shown.

### Answers

The** area of the circle** is approximately **4.52 square kilometers**.

To find the **area of a circl**e with **radius **1.2 kilometers, we can use the formula:

Area = π × [tex]r^{2}[/tex]

Plugging in the values we get:

Area = 3.14 ×[tex]1.2^{2}[/tex]

Area = 3.14 × 1.44

Area = 4.5216

Rounding to the nearest hundredth, we get:

Area ≈ 4.52 square kilometers

The area of a circle is the measure of the region enclosed by the circle in a** two-dimensional space**. It is the amount of space inside the circle and is usually measured in square units, such as square meters, square feet, square centimeters, etc. The formula for calculating the area of a circle is A =[tex]\pi r^{2}[/tex]

, where A is the area, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14. In simpler terms, the area of a circle is the** total surface** area of the circle, including the interior region, and is directly proportional to the square of its radius.

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the complete questionis :

determine the area of the solution, use 3.14 as [tex]\pi[/tex] value and round the answer to the nearest hunderedth.

a circle with radius 1.2km is shown

A hat store has a promotion where all hats cost 80% of their original price. If you bought

a hat that cost $16, what is the original price before the promotion?

### Answers

**Answer: The original price is $17.98**

**Step-by-step explanation:**

20

hope this helps pls heart my answer

The shop has a necklace of 41 pearls for sale, with the middle pearl being the largest and most expensive. Moving from the middle pearl towards each end of the coil, each subsequent pearl is cheaper than the previous one by one and the same amount. The most expensive pearl costs 55 euros, and the following pearls cost 52 euros. a) How much does one of the cheapest pearls cost? b) How much does this necklace cost, i.e. all the pearls together? c) One of the pearls in the necklace developed a crack and the price of this pearl decreased by 1/5. The price of the necklace therefore decreased by 6.5 euros. How much was this pearl before the crack?

### Answers

The original **price** of the pearl was 52 euros.

What is price?

Price is the **monetary value** of a product, service, or asset. It is one of the most important **factors** in a customer's decision to purchase something. Price also determines the amount of profit a business makes on a particular product or service. Price is a key component of the marketing mix, and it can be used to create a sense of value for customers. Price can also be used to differentiate a product from competitors, as well as to indicate quality levels and to create loyalty.

a) One of the cheapest pearls costs 41 euros.

b) This necklace costs 2153 euros, which is the sum of all the pearls.

c) The pearl with the crack originally cost 52 euros. The price was reduced by 1/5, which is 10.4 euros, making the price of the pearl 41.6 euros. The decrease in price of the necklace was 6.5 euros, which means the reduction in price of the pearl was 6.5 euros. Therefore, the original price of the pearl was 52 euros.

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There are 15C5 or 3003 possible combinations in the sample space.There are 20C5 or 15504 **possible combinations** in the sample space.

What is number?

A **number** is a mathematical object used to count, measure, and label. Numbers can be represented in many different forms such as natural numbers, **integers**, real numbers, and complex numbers. They can also be classified as scalar numbers (which have a magnitude or value only) or vector numbers (which have both magnitude and direction). Numbers can be used to represent many different things, including measurements, distances, money, and quantities.

A. Sample space: The sample space for this experiment is the set of all possible combinations of 5 questions that can be selected from 15 questions. This can be calculated as follows: 15 choose 5 = 15!/(5!×10!) = 3003. Therefore, the total number of sample points in the sample space is 3003.

B. Sample space: The sample space for this experiment is the set of all possible combinations of 5 members that can be selected from the 20-member membership. This can be calculated as follows: 20 choose 5 = 20!/(5!×15!) = 15504. Therefore, the total number of sample points in the sample space is 15504.

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suppose a female fruit fly heterozygous for the white (w) gene is mated to a male with wild type red eye color. the white gene is x-linked, so the cross can be written as: xw xw x xw y. what is the the probability of getting a fly that is white-eyed and male?

### Answers

The **probability** of getting a fly that is white-eyed and male from the given cross is **25%**.

Let's see how: The cross of a female fruit fly heterozygous for the **white (w)** gene with a male having the wild type red eye color can be written as: xw, xw, x, xw, y.

As per the given cross, the female parent can have two types of gametes, i.e., xw and x. The male parent can have two types of gametes, i.e., xw and y.

The** possible offsprings** are:xw, x (white-eyed female)

xw ,y (red-eyed male)

x ,xw (white-eyed female)

y, xw (red-eyed male)

So, there are two white-eyed females and two red-eyed males in the offspring. Out of these four, only one is a white-eyed male.

Hence, the **probability** of getting a fly that is white-eyed and male is 1/4, or 25%.

Therefore, the **probability** of getting a fly that is white-eyed and male from the given cross is 25%.

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if you're given a jar with a mix of fair and unfair coins, and you pull one out and flip it 3 times, and get the specific sequence heads heads tails, what are the chances that you pulled out a fair or an unfair coin

### Answers

The **probability** of pulling out a fair or an unfair coin cannot be determined unless the probability of obtaining heads on an unfair coin toss and the proportion of unfair coins in the jar is known.

Let p be the probability of obtaining heads on a fair coin toss. Since the coin is fair, p = 1/2. Thus, the probability of obtaining the sequence heads, heads, tails on a fair coin toss is:

p × p × (1 - p) = (1/2) × (1/2) × (1/2) = 1/8

Therefore, the probability of pulling out a fair coin is 1/8.

Let q be the probability of obtaining heads on an **unfair** coin toss. Since the coin is unfair, q ≠ 1/2. Thus, the probability of obtaining the sequence heads, heads, tails on an unfair coin toss is:

q × q × (1 - q)

Therefore, the probability of pulling out an unfair coin is:

Probability of pulling out an unfair coin = (Probability of obtaining the sequence heads, heads, tails on an unfair coin toss) × (Probability of choosing an unfair coin)

= q × q × (1 - q) × P (unfair)

Thus, the probability of pulling out a fair coin or an unfair coin is:

Probability of pulling out a fair or an unfair coin = 1/8 + q × q × (1 - q) × P (unfair).

Therefore, the **probability** of pulling out a fair or an unfair coin cannot be determined unless the probability of obtaining heads on an unfair coin toss and the proportion of unfair coins in the jar is known.

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The base of a solid is bounded by the graph of x^2 + y^2 = a^2, where a>0. Find the volume of the solid if every cross section perpedicular to the x-axis is a square.

### Answers

this is just a quick addition to the good posting above by "s157778"

Check the picture below.

The **volume **of the **solid **is, 8a³/3.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, To find the **volume **of the solid, we first need to determine the limits of integration.

Since the cross sections are **perpendicular **to the x-axis, we will integrate with respect to x.

Let's consider a **cross section** of the solid at a particular value of x, which we will call x₀.

This cross section is a square, so its area is given by the side length squared.

The side **length **of the square is equal to the distance between the y-values where the graph of x² + y² = a² intersects the line x = x₀

Now, Using the equation of the circle, we can solve for y in terms of x:

y² = a² - x²

y = ± √(a² - x²)

Hence, The **distance **between these two y-values is therefore:

⇒ √(a² - x²) - (-√(a² - x²))

= 2√(a² - x²)

So, the area of the cross section at x = x₀ is:

Area = (2 √(a² - x²))²

= 4(a² - x²)

To find the volume of the **solid**, we integrate this area with respect to x from -a to a:

⇒ Volume = ∫[-a,a] 4(a² - x²) dx

= 4a² ∫[-a,a] dx - 4 ∫[-a,a] x² dx

= 8a³/3

Therefore, The **volume **of the **solid **is, 8a³/3.

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Your friend asks you to help her babysit and will pay you 3 pennies for the first job. You agree to help if she triples your payment for each job completed. After 2 jobs, you will receive 9 pennies, and after 3 babysitting jobs, you will receive 27 pennies.

Complete and solve the equation that finds the number of pennies she will pay you after the 9th babysitting job.

### Answers

**Answer:**

if it triples each time you will get 19683 pennies

**Step-by-step explanation:**

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a deck of cards is dealt out. what is the probability that the 14th card dealt is an ace? what is the probability that the first ace occurs on the 14th card?

### Answers

The **probability** of picking an ace on any draw is 4/52 or 1/13.

The **probability** that the 14th card dealt is an ace is 0.002641

We can first calculate the **probability** of not getting an ace on the first 13 draws, and then find the probability of getting an ace on the 14th draw:

P(No ace on 1st draw) = 48/52

P(No ace on 2nd draw) = 47/51

P(No ace on the 3rd draw) = 46/50

And so on...

P(No ace on the 13th draw) = 36/40.

P(Ace on 14th draw) = 4/39

To find the probability of these** independent events**, we multiply their **probabilities**:

P(Ace on 14th draw) = P(No ace in first 13 draws) x P(Ace on 14th draw)

P(Ace on 14th draw) = (48/52) x (47/51) x ... x (4/40) x (4/39)

P(Ace on 14th draw) ≈ 0.002641

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a sample set of weights in pounds are 1.01, .95, 1.03, 1.04, .97, .97, .99, 1.01, and 1.03. assume the population of weights is normally distributed. find a 99 percent confidence interval for the mean population weight.

### Answers

The 99 percent **confidence interval** for the **mean** population weight is (1.002, 1.022).

To find a 99 percent **confidence interval** for the **mean** population weight, you can use the following formula:

Confidence Interval = Mean ± (Standard Error * Critical Value)

Where:

Mean = (Sum of all the values)/ (Number of values)Standard Error = Standard Deviation / Square Root of (Number of values)Critical Value = The Z-Score for the 99th percentile

In this case, the Mean = (1.01 + .95 + 1.03 + 1.04 + .97 + .97 + .99 + 1.01 + 1.03) / 9 = 1.012

The Standard Deviation = 0.03

The Square Root of 9 is 3

The Z-Score for the 99th percentile is 2.576

Therefore, the 99 percent confidence interval for the mean population weight is 1.012 ± (0.03 / 3 * 2.576) = (1.002, 1.022).

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NEED HELP NOW!!!!!!!!

Which table represents a linear function?

1.

x y

-7 0

-4 2

2 6

5 8

2.

x y

3 -1

5 -2

4 -3

7 -2

3.

x y

-4 1

2 3

4 1

6 5

4.

x y

-3 2

1 0

2 2

4 6

### Answers

The **linear function **in the list of options is the table 1

Identifying the linear function

A **function **is linear if it has a constant rate of change, which means that the change in y for any two points is **proportional** to the change in x.

This is the same as saying that the function's graph is a **straight line**.

For table 1

The **rate of change **between (-7,0) and (-4,2) is (2-0)/(−4+7)=2/3. The **rate of change** between (-4,2) and (2,6) is (6-2)/(2+4)=4/6=2/3.This is the same for other pairs

Therefore, the first **table** represents a linear **function**.

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Can someone pretty please help me

### Answers

**Answer:** 3

20(2)-1/13

40-1/13

39/13=3

**Step-by-step explanation:**

Hope this helps!! Mark me brainliest!!

So we can just plug in the values

20(2)-1/13

40-1= 39

39/13 this can be simplified to 3

a bank in alice springs (australia), also known as alice, wants to send a lot of financial data to the bank of baltimore, also known as bob. they want to use aes, but they do not share a common key. all of their communications will be on public airwaves. describe how alice and bob can accomplish this using rsa.

### Answers

To securely send** data **using AES, Alice and Bob can utilize RSA for key exchange. RSA is a public-key cryptosystem, which means that each party has a public and **private key**.

To initiate the key exchange, Bob generates a public and private key and sends his **public key** to Alice. Alice then encrypts the AES key with Bob's public key and sends it back to Bob. Since only Bob has the private key, only he can decrypt the **message** and obtain the AES key.

Alice and Bob can now use the AES key to encrypt and decrypt their financial data. This ensures that even if someone intercepts their **communication** on public airwaves, the data remains secure since the AES key is only known to Alice and Bob.

It is important to note that RSA is used only for the key exchange, not for encrypting the data itself.

The** data **is encrypted using AES, which is much faster and more efficient than RSA for large amounts of data.

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Show a way to count from 68 to 130 using tens and ones

### Answers

**Answer:**

69,70,80 90,100,110,120,130

40 12 40

Cost $74 $27 $76

Part A: Calculate the corresponding unit rate for each package

### Answers

a. The corresponding **unit rate **of Dog Cakes, Bark Bits, and Woofy Waffles for each package is $1.85 per pound, $2.25 per pound, and $1.90 per pound respectively.

b. The best buy using the unit rates found in Part A is $1.85 per pound.

Part A: We divide the cost by the size to determine the unit pricing for each package.

**Dog Cakes**: The unit price is $74 divided by 40 pounds or $1.85 per pound.

Bark Bits: $27 divided by 12 pounds equals $2.25 per pound.

Unit pricing for **Woofy Waffles** is $76 divided by 40 pounds or $1.90 per pound.

Part B: We compare unit pricing to get the best purchase. The greatest deal is the package with the lowest unit price. The greatest deal in this situation is Canine Cakes, which has the lowest unit price at $1.85 per pound.

Even though Canine Cakes and Woofy Waffles have the same size (40 pounds), Canine Cakes has a cheaper unit rate than Woofy Waffles. The product with the highest unit rate is **Bark Bits**, making it the most costly per pound. Canine Cakes is the greatest purchase based on unit prices.

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The question is -

Jeremiah needed dog food for his new puppy. He compared the prices and sizes of three types of dog food.

Canine Cakes Bark Bits Woofy Waffles

Size (pounds) 40 12 40

Cost $74 $27 $76

Part A: Calculate the corresponding unit rate for each package.

Part B: Determine the best buy using the unit rates found in Part A. Explain your answer.

suppose the A is a 3x8 matrix tht has an echelon form with two zero rows. find the dimension of the row space of A, the dimension of the column space of A, and the dimension of the null space of A.

dimension of the row space of A =

dimension of the column space of A=

dimension of the null space of A=

### Answers

The **dimension** of the row space of A is 1, the dimension of the column space of A is 3, and the dimension of the null space of A is 5.

Since A has an echelon form with two zero rows, it means that there are only two nonzero **rows** in A. Therefore, the row space of A is spanned by a single nonzero row, which implies a dimension of 1.

On the other hand, A has three columns, and since the echelon form of A implies that there are no pivot **columns** beyond the first two, the column space of A is spanned by the first two columns. Thus, the dimension of the column space is 2.

Finally, since A has 5 columns with no pivot, the dimension of the null space of A is 5, by the dimension formula (i.e., the nullity of A plus the rank of A equals the number of columns in A).

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Assuming you use 12 kg of cornice cement per 100 m of cornice, how many kilograms of cornice cement do you need for 93 m of cornice

### Answers

**11.16 kg** of cornice cement is needed for 93 **meters** of cornice. To calculate the amount of cornice **cement** required for 93 meters of cornice, we can use a proportion:

12 kg of cornice cement is required for 100 m of cornice.

Therefore, we can set up the following **equation** to solve for the amount of **cornice** cement required for 93 meters:

12 kg / 100 m = x kg / 93 m

To **solve** for x, we can cross-multiply:

12 kg x 93 m = 100 m x

x = (12 kg x 93 m) / 100 m

**x = 11.16 kg**

Therefore, 11.16 kg of cornice cement is needed for 93 **meters** of cornice.

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(a) Find the greatest common factor (GCF) of 6 and 2.

GCF = ☐

(b) Use the GCF to factor 6 - 2.

6 - 2 = ☐ × (☐ - ☐)

### Answers

**Step-by-step explanation:**

(a) The greatest common factor (GCF) of 6 and 2 is 2.

(b) Using the GCF of 2, we can factor 6 - 2 as follows:

6 - 2 = 2 × 3 - 2

= 2 × (3 - 1)

= 2 × 2

Therefore, 6 - 2 = 2 × 2.

Which day did Walker read the fastest? a) Day 1 - 20 pages in 35 minutes b) Day 2 - 80 pages in 15 minutes c) 46 pages in 65 minutes d) 35 pages in 26 minutes

### Answers

**Answer:**

b) Day 2-80 pages in 15 minutes

The thicknesses of 13 randomly selected linoleum tiles were found to have a standard deviation of 4.76. Construct the 90% confidence interval for the population standard deviation of the thicknesses of all linoleum tiles in this factory. Round your answers to two decimal places.

### Answers

The 90% **confidence interval** for the population standard deviation of the thicknesses of all linoleum tiles in this factory is (2.16, 9.80), rounded to two decimal places.

To compute the 90% confidence interval for the population **standard deviation** of the thicknesses of all linoleum tiles in this factory, we have to make use of the **Chi-square** distribution.Assuming a level of significance of α=0.10, and a sample size of n = 13, we have:(n-1)S^2 / σ^2 = χ^2_(0.05, 12)

Here, S is the sample standard deviation, σ is the population standard deviation, and χ^2_(0.05, 12) represents the critical value of the Chi-square **distribution** at α/2 = 0.05 for 12 degrees of freedom, which is 19.68. Let's substitute these values into equation (1):(13 - 1)(4.76^2) / σ^2 = 19.68By simplifying the above **equation**, we get:σ = sqrt[(13 - 1)(4.76^2) / 19.68]σ ≈ 5.00

Thus, we can **compute **the 90% confidence interval as follows:(4.76√12/χ^2_(0.05,12),4.76√12/χ^2_(0.95,12)) = (2.16,9.80)

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Which statement best compares the shapes of the

distributions of the quiz scores for the two classes?

Both distributions appear to be fairly symmetric.

O The distribution of quiz grades for class 1 appears to

be skewed left, and the distribution of quiz grades for

class 2 appears to be fairly symmetric.

O The distribution of quiz grades for class 1 appears to

be skewed right, and the distribution of quiz grades

for class 2 appears to be fairly symmetric.

O The distribution of quiz grades for class 1 appears to

be skewed right, and the distribution of quiz grades

for class 2 appears to be slightly skewed left.

### Answers

2. the **distribution** of quiz grades for class 1 appears to be skewed right, and the distribution of quiz grades for class 2 appears to be fairly symmetric.

What is a distribution?

A distribution is **skewed right** when the tail of the distribution extends to the right, indicating that the data are more spread out on the right side of the distribution than on the left. Conversely, a distribution is considered to be skewed left when the tail of the distribution extends to the left, indicating that the data are more spread out on the left side of the distribution than on the right.

In this case, the distribution of quiz grades for class 1 appears to be skewed right, indicating that the data are more spread out on the right side of the distribution than on the left. The distribution of quiz grades for class 2 appears to be fairly **symmetric**, indicating that the data are equally spread out on both sides of the distribution.

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suppose there are 10 students in a class. how many ways are there to choose 2 students from this group of 10 students?

### Answers

The** number of ways** in which 2 students from this group of 10 students are selected is 90 ways.

Define about the arrangements?

Generally speaking, an** arrangement **of elements is just a collection of them. The sequence of the n items has no bearing on the number possible "arrangements" that can be made of them (order is significant).

A permutation is an arrangement (of ordering) of a collection of items.A sequence is a grouping of any items or a collection of numbers in a specific order that adheres to some norm.An arrangement with lines or shapes is referred to as a pattern, particularly a design whereby a single shape is repeated throughout a surface at regular intervals.

Total students = 10.

So, the first student can be selected from all 10 students.

= 10 ways.

Now, total students left = 9.

So, the second student can be selected from all 10 students.

= 9 ways.

number of ways = 10*9 = 90 ways.

Thus, number of ways in which 2 students from this group of **10 students **are selected is 90 ways.

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